Search: id:A035363
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%I A035363
%S A035363 1,0,1,0,2,0,3,0,5,0,7,0,11,0,15,0,22,0,30,0,42,0,56,0,77,0,101,0,135,
%T A035363 0,176,0,231,0,297,0,385,0,490,0,627,0,792,0,1002,0,1255,0,1575,0,1958,
%U A035363 0,2436,0,3010,0,3718,0,4565,0,5604,0,6842,0,8349,0,10143,0,12310,0
%N A035363 Number of partitions of n into even parts.
%C A035363 Convolved with A036469 = A000070 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Jun 09 2009]
%C A035363 Note that these partitions are located in the head of the outer shell 
               of the partitions of n (See A135010). [From Omar E. Pol (info(AT)polprimos.com), 
               Nov 20 2009]
%F A035363 G.f.: prod(1/(1-x^k), k even)
%F A035363 Convolution with the number of partitions into distinct parts (A000009, 
               which is also number of partitions into odd parts) gives the number 
               of partitions (A000041). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jan 06 2006
%F A035363 If n is even then a(n)=A000041(n/2) otherwise a(n)=0. [From Omar E. Pol 
               (info(AT)polprimos.com), Nov 20 2009]
%p A035363 ZL:= [S, {C = Cycle(B), S = Set(C), E = Set(B), B = Prod(Z,Z)}, unlabelled]: 
               seq(combstruct[count](ZL, size=n), n=0..69); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 26 2008
%Y A035363 Subsequence a(2n) is simply the partition numbers A000041.
%Y A035363 First column (m=0) of triangle A103919.
%Y A035363 A036469, A000070 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 09 
               2009]
%Y A035363 Sequence in context: A008820 A066682 A049641 this_sequence A079977 A008799 
               A011013
%Y A035363 Cf. A135010, A138121. [From Omar E. Pol (info(AT)polprimos.com), Nov 
               20 2009]
%Y A035363 Adjacent sequences: A035360 A035361 A035362 this_sequence A035364 A035365 
               A035366
%K A035363 nonn,easy,new
%O A035363 0,5
%A A035363 Olivier Gerard (olivier.gerard(AT)gmail.com)

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